The present invention relates to a method and system for dispersion compensation of optical signals. In particular, the present invention relates to a method for higher-order dispersion compensation using at least two chirped Bragg gratings to selectively tune the reflection points of two polarization resolved signals, creating a variable higher-order dependent delay.
Present day telecommunication systems require that optical signals be conveyed over very long distances. In an optical communications signal, data is sent in a series of optical pulses. Signal pulses are composed of a distribution of optical wavelengths and polarizations, each of which travels at its own characteristic velocity. This variation in velocity leads to pulse spreading and thus signal degradation. Degradation due to the wavelength dependence of the velocity is known as chromatic dispersion, while degradation due to the polarization dependence is known as polarization mode dispersion (PMD).
Mathematically, the velocity of light ν in a waveguide is given by                     v        =                  c          n                                    (        1        )            where c is the velocity of light in free space and n is the effective index of refraction in the waveguide.
Normally, the effective index, n, of the optical medium is dependent upon the wavelength of the light component. Thus, components of light having different wavelengths will travel at different speeds.
In addition to being dependent upon wavelength, the effective index in a waveguide also may be dependent upon the polarization of the optical signal. Even in “single-mode” fiber, two orthogonal polarizations are supported and, in the presence of birefringence, the polarizations travel at different speeds. Birefringence in the fiber may arise from a variety of sources including both manufacturing variations and time-dependent environmental factors. The speed difference results in a polarization-dependent travel time or “differential group delay” (DGD) between the two different polarization modes within the birefringent fiber. In real optical fiber systems, the magnitude of birefringence and the orientation of the birefringent axes vary from place to place along the fiber. This results in a more complex effect on the optical signal, which is characterized by the concept of “principal states of polarization” or PSPs. PSPs are defined as the two polarization states that experience the maximum relative DGD, and they uniquely characterize the instantaneous state of the system.
Polarization mode dispersion (PMD) is measured as the distortion arising from the statistical sum of the different group velocities of the two components of polarization as the signal propagates through the different sections of the optical communications system. PMD includes first order PMD and higher-order PMD and is non-deterministic. First order PMD is the differential polarization group delay at a given wavelength. The instantaneous value for a long fiber may vary over both long time intervals, due to slow variations such as temperature drift, and short time intervals, due to fast variations such as mechanical vibration induced polarization fluctuations. The coefficient describing the mean value of first order PMD may vary from more than 2 ps/km1/2 for relatively poor PMD performance fiber to less than 0.1 ps/km1/2 for relatively good PMD performance fiber.
Second order PMD arises mainly from two sources: i.) a first order PMD that varies with wavelength; ii.) a change of the system PSP (principal state of polarization) orientation with wavelength, which results in a variation of PMD with wavelength. Second order PMD results in a wavelength dependent group delay, which is equivalent in effect to variable chromatic dispersion, and can have either a negative or positive sign. The speed of fluctuation is on the same order as the speed of fluctuation of first order PMD.
There are two types of chromatic dispersion: deterministic and variable. Deterministic dispersion is the set chromatic dispersion per unit length of waveguide having a fixed index of refraction. Deterministic dispersion is relatively fixed (e.g., ˜17 ps/nm*km for standard single mode fiber) for a given set of environmental conditions. For example, 17 ps/nm*km means that a ten kilometer (10 km) system, carrying data with a bandwidth of 0.1 nanometers (nm), will experience approximately 17 picoseconds (Ps) of chromatic dispersion.
Variable chromatic dispersion is caused by changes in fiber link length, due to adding or dropping channels for example, and by tensile stresses and/or fluctuations in temperature. Reasonable values to be expected for the amount that the chromatic dispersion will change are in the range −500 ps/nm to +500 ps/nm.
In addition to the effects of PMD and chromatic dispersion alone, there is a higher-order dispersion cross term that arises from the simultaneous presence of both chromatic dispersion and PMD. This cross term between chromatic dispersion and second order PMD has a mean value of zero, but may have a non-zero root-mean-square (RMS) contribution. Similarly to second order PMD terms, the RMS value may have a positive or negative contribution. The magnitude of the RMS contribution may vary from less than 1% of the chromatic dispersion to the same order as the chromatic dispersion, depending on the PMD coefficient of the fiber.
Dispersion imposes serious limitations on transmission bandwidth, especially across long distances, such as in transoceanic routes. Dispersion issues become much more important at higher bit rates, where the separation between the optical pulses is less and where shorter pulses result in a wider signal spectral bandwidth, exacerbating chromatic and higher-order PMD effects. At bit rates greater than or equal to 40 Gb/s, even for “good” fiber (≲0.1 ps/km1/2 PMD coefficient), long length links are deemed to require higher-order dynamic compensation. Dispersion may become an inhibiting factor either limiting overall system length or increasing system costs due to the need for additional optical-to-electrical-to-optical signal conversion sites to permit electrical signal regeneration.
Higher-order dispersion has not been adequately recognized, measured and addressed in past dispersion compensation devices. An understanding of the sources and factors in higher-order dispersion is important in providing a higher-order dispersion compensation solution.
Exemplary calculations for a “good” fiber (PMD coefficient of 0.1 ps/km1/2) show:
Chromatic Dispersion term:17ps/nm*kmFirst order PMD coefficient:0.1ps/km1/2Second order PMD coefficient:0.006ps/nm*kmCross term RMS magnitude:0.37ps/nm*kmExemplary calculations for a “poor” fiber (1 ps/km1/2) show:
Chromatic Dispersion term:17ps/nm*kmFirst order PMD coefficient:1ps/km1/2Second order PMD coefficient:0.6ps/nm*kmCross term RMS magnitude:3.7ps/nm*km
The second order coefficient of PMD may be calculated based on the theory described in “Second-Order Polarization Mode Dispersion: Impact on Analog and Digital Transmissions,” IEEE J. of Lightwave Tech., JLT-16, No. 5, pp. 757–771, May 1998, which is hereby incorporated by reference.Second order PMD coefficient=(First order PMD coefficient)2/1.73  (2)
Equation 2 only accounts for the root-mean-square (RMS) of the resulting chromatic dispersion. The cross term was calculated to be:Cross term=(17)1/2*(First order PMD coefficient)1/2*1.16  (3)
Therefore, it may be appreciated that for fiber that has a high PMD coefficient, PMD may cause a problem when only fixed chromatic dispersion compensation is used due to accumulated chromatic dispersion through the second order PMD term and the cross term. This leads to a high value of uncompensated dispersion as fiber PMD coefficients become larger or as the bit rate gets higher.
From this analysis, it may be calculated that even using the best of fiber produced today (assuming ˜0.025 ps/km1/2), propagation distances are likely limited to ≲3000 km (dispersion<0.3*100 ps) for 10 Gb/s transmission and ≲200 km (dispersion<0.3*25 ps) for 40 Gb/s without performing dynamic chromatic dispersion compensation to eliminate the effects of the 2nd order PMD and cross terms.
A number of literature articles attempt to address the issue of higher-order dispersion compensation. One approach is to use a multi-section PMD compensator. Such an approach is likely to be expensive and also will be limited in the amount of variable chromatic dispersion compensation available. Another approach is to selectively add specific chirps to various portions of the pulse and to send the pulse through a high dispersion element with the correct sign to compress the pulse. Such an approach may account for all types of dispersion. However, such an approach is likely to be expensive due to the need for clock recovery and phase modulation and also only may be useable at the receiver terminal. Furthermore, it only may work if the residual dispersion is low.
The need remains for a dispersion compensation system that dynamically adjusts not only for PMD, but also for chromatic dispersion and higher-order dispersion. Increased telecommunications system requirements, such as the need to compensate for fluctuations in temperature and the possibility of variable path lengths due to the optical add/drop systems envisioned in the near future, call for a compensation system that is dynamic and cost-efficient.